Section 6-8
Monomial Factors of Polynomials
To factor a common monomial factor from a polynomial, it is sometimes helpful to write out the complete prime factorization of each term.
Example:
Factor:
56q3 + 42q5
Write out the complete factorization of each term.
56q3 + 42q5 = (2 · 2 · 2 · 7 · q · q · q) + (2 · 3 · 7 · q · q · q · q · q)
Identify common factors in each term (shown in red).
= (2 · 2 · 2 · 7 · q · q · q) + (2 · 3 · 7 · q · q · q · q · q)
Use the distributive property.
= (2 · 7 · q · q · q)(2 · 2 + 3 · q · q)
= 14q3(4 + 3q2)
